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Chapter 27The Tools of Finance

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Time Value of Money

A dollar received in the future does not have the same purchasing power as a dollar today

Why? Inflation Interest helps dollars grow to maintain

their purchasing power

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Simple Interest

Principle x Rate x Time Principle is an amount borrowed or

invested Rate is the annual rate of interest paid or

earned Time is a function of one year

If you invest $10,000 for one year at 6%

10,000 x .06 x 1 = $600 10,000 x .06 x 4 = $2,400 for four

years At the end of four years you have

$12,400

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Compound Interest

Interest earning interest What if the interest earned each year is

allowed to grow as part of the investment?Yr 1: 10,000 + (10,000 x .06 x 1) = 10,600Yr 2: 10,600 + (10,600 x .06 x 1) = 11,236Yr 3: 11,236 + (11,236 x .06 x 1) = 11,910Yr 4: 11,910 + (11,910 x .06 x 1) = 12,625

You come out ahead by $225

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Compound Interest

Compound interest is an exponential function: the bigger it gets the faster it grows

Future value = Present value x (1 + r)n

FV = $10,000 x (1 + .06)4

FV = $12,625

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Variables

Present Value (PV) The value of an investment or amount borrowed today Principle only, no time no interest

Future Value (FV) Principle + interest at some time in the future

N is the number of compounding periods R is the interest rate per compounding period

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Compounding vs. Discounting

Compounding is the process of adding interest: take a present value or principle payments and add interest to arrive at a future value

FV = PV x (1+r)n

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Compounding vs. Discounting

Discounting moves in the opposite direction: take a future value with principle and interest and remove the interest

PV = FV /(1+r)n

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Other Considerations

Risk aversion Diversification (firm-specific risk vs.

market risk) Risk vs. Return Asset valuation

Value & Price Capital gains & dividends Random walk & index funds

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Case Study: Enron

May 2010